Question

If the car moves for equal times along the road and hill, create an expression for its average velocity vector v(ave) in terms of v0x, V1x, and v1y during the total time interval and unit vectors i and j

Answer 1

The average velocity vector of the car, v(ave), is the simple average of the initial and final velocity vectors multiplied by the unit vectors i and j for the horizontal and vertical components, respectively, under the assumption of constant acceleration.

Step-by-step explanation:

To find the average velocity vector v(ave) of the car when it moves for equal times along the road and up the hill, we can use the definition of average velocity. The average velocity vector is the total displacement vector divided by the total time. Assuming the car spends equal amounts of time on the road and hill sections, and given the velocities v0x, V1x, and v1y, we can write the average velocity vector as:

v(ave) = ½(v0 + v1) = ½(v0x·i + (V1x·i + v1y·j))

Here, i and j are the unit vectors in the horizontal and vertical directions respectively. The factor of ½ arises because we are taking the simple average of initial and final velocity vectors for the time intervals. This assumes constant acceleration.

Answer 2

So here in order to find the average velocity we can say

`v_(avg) = (displacement)/(time)`

so first we know that along the horizontal and along the inclined it moves with same time interval

so here we will have displacement in x direction as

`x = v_o (t) + v_(1x)(t)`

now the average velocity in x direction will be given as

`v_(avg) = (v_o t + v_(1x) t)/(t + t)`

`v_(avg) = (v_o + v_(1x))/(2)`

now similarly for y direction

first we will find its displacement

`y = v_(1y)(t)`

now the average velocity in y direction will be given as

`v_(avg) = (v_(1y) t)/(t + t)`

`v_(avg) = (v_(1y))/(2)`

now net velocity is given as

`v_(avg) = (v_o + v_(1x))/(2)\hat i + (v_(1y))/(2)\hat j`